Using morph targets with multiple meshes
You can 'join as shapes' two meshes, as long as they have equal number of vertices.

Select first the model with the morph and then the base model (shift+click); in the Shapes Keys panel click the arrow (triangle) and select 'Join as Shapes'.



This will create a Basis key, if the model doesn't have one already, and a key named as the source model (by default is set to 0, I set it to 1 in the image to show the result).